Unlike conventional reservoirs, pores in shale formations are extremely small, typically on the order of nanometers. In these nano pores, a non-negligible portion of gas molecules collides more often with the pore wall than with other molecules, and thus so-called “slip flow” and Knudsen diffusion occur. Previous studies on gas flow in shale matrix found that the gas permeability in shale is a function of the pore gas pressure because the slip flow and Knudsen diffusion effect becomes significant when the pore gas pressure is relatively low (for example thousand pounds per square inch or lower).
Shale gas permeability as a function of pore gas pressure, resulting from “slip flow” and diffusion processes, is critical for characterizing and modeling gas flow in a shale gas reservoir. However, this important pore gas pressure-dependency is hardly considered in practice because of the lack of a practical and efficient technique that can be used routinely for determining the pressure-dependent shale gas permeability.
Pressure dependence has a significant impact on predicted gas-production rate. There are currently two approaches to measure the pressure dependence of gas permeability in the laboratory. The first one is to simply perform a number of pulse-decay permeability tests under different gas pressures. Then, these tests will provide gas permeability values for a number of gas pressures. Initially, the system is in equilibrium with a given gas pressure. A small pressure pulse is then introduced into the upstream gas reservoir such that the pulse does not have a significant disturbance to the gas pressure in the system. The pressures at the two gas reservoirs are monitored as a function of time. The pressure evolution results are fitted using analytical solutions with permeability being a fitting parameter. However, it generally takes a relatively long time to equilibrate the test system from one test pressure to the next one.
The other approach to determine the pressure dependence is to first develop a formulation of gas permeability as a function of gas pressure and then estimate values for parameters in the formulation by numerically matching the relevant test results under different gas pressure conditions. Test results are generally different from pulse-decay tests in which the pressure pulse is not limited to a small one because numerical model is flexible enough to incorporate the pulse disturbance to the system. However, non-uniqueness of parameter estimation is always a problem for inverse modeling. Also, the accuracy of estimated results from this approach is ultimately determined by that of the used formulation of gas permeability as a function of gas pressure that is not fully established yet.